I purchased an ebook in Mobi format from a seller other than Amazon. I used the Send to Kindle application on my PC to send it to my Kindle device (strangely, by Kindle for PC was not on the list of options - more on this later). It was delivered to my device right away, and I happily read it. I made many highlights (as I often do), and I wanted to see those highlights on my PC to prepare some teaching notes. However, I discovered that the book did not appear on my Kindle for PC. I also checked my history of highlights at https://kindle.amazon.com/your_highlights and they were not there either. I started to worry at this point, thinking that I only ever have access to my highlights on the Kindle device itself.
I called Amazon support and here's what we learned: we went to Manage Your Content and Devices and clicked on YOur Content. The book did not appear under books, but DID appear under Docs. I then clicked on the action button next to my book and clicked the Deliver to: Others link. This brought up a window with a drop-down list of all my devices - except my Kindle for PC or the Amazon Cloud Reader were greyed out. I picked my iPhone, and sure enough the book appeared there with my highlights (yay!). I then went to my iPad (without sending the book there explicitly) and it was there with my highlights again.
Short version: If you send a third-party mobi book to your kindle, it will sync between Kindle apps, but only if they are on a Kindle, iOS or Android device; the cloud reader and PC applications (maybe Mac, too?) will not have the book or its associated notes/highlights.